Been there, done that
On the one hand, my students never fail to surprise me. On the other, they can't help replaying the evergreen mistakes of the past. They have certain recurring problems.
Yes, I know it may be on the verge of becoming a lost art, but in most math classes you still need to write stuff. By hand. We don't (yet) allow you to submit your answers by texting. You have to write stuff on paper. If you can't read your own writing, you are in big trouble. Each semester I inveigh against sloppy writing practices that permit students to confuse their own symbols with each other. I have students who sometimes cannot tell the difference between their own 4's and 9's. Their own 3's and 8's. And, of course, their own z's and 2's.
It is that last problem that just manifested itself in a big way again. As before, it sabotaged a student as she was trying to solve an equation for the variable z. The results are similarly disastrous.
The problem involved a proportion containing an unknown. As you can see, the student briskly applied cross-multiplication, even indicating her calculation with swoopy arrows to mark the source of her factors. Unfortunately, the product of 2 and z magically morphed into 4. When she copied the proportion, she wrote 2 and z as indistinguishable (even to her) symbols.
Careless handwriting is hardly the entire story. Faced with a nonsensical equation stating that 40 equals 4, she promptly divided both sides by 4. She concluded that the answer had to be 10, which she promptly wrote in the answer blank. Funny. Why didn't she pick 1? Perhaps because in her experience 1 is so seldom the answer. The 10 just looks better.
Of course, “looking better” is an odd criterion for someone who can't even read her own writing.